"uuid","repository link","title","author","contributor","publication year","abstract","subject topic","language","publication type","publisher","isbn","issn","patent","patent status","bibliographic note","access restriction","embargo date","faculty","department","research group","programme","project","coordinates"
"uuid:4d488d96-4ca9-492a-8260-dfb07ff0e8ce","http://resolver.tudelft.nl/uuid:4d488d96-4ca9-492a-8260-dfb07ff0e8ce","Finding starting points analytically for optical system optimization","Bociort, F.; van Grol, P.","","2012","Understanding the structure of the design space in optical system optimization is difficult, because common human intuition fails when it encounters the challenge of high dimensionality, resulting from the many optimization parameters of lens systems. However, a deep mathematical idea, that critical points structure the properties of the space around them, is fruitful in lens design as well. Here we discuss simple systems, triplets with curvatures as variables, for which the design space is still simple enough to be studied in detail, but complex enough to be non-trivial. A one-to-one correspondence between the possible design shapes and the critical points resulting from a simplified model based on third-order spherical aberration within the framework of thin-lens theory could lead in the future to a new way to determine good starting points for subsequent local optimization.","saddle point; critical point; global optimization; optical system design","en","conference paper","SPIE","","","","","","","","Applied Sciences","ImPhys/Imaging Physics","","","",""
"uuid:370b044e-f491-4a14-8717-07724cb5343e","http://resolver.tudelft.nl/uuid:370b044e-f491-4a14-8717-07724cb5343e","Systematics of the design shapes in the optical merit function landscape","Bociort, F.; Van Grol, P.","","2010","In this paper we describe new properties of the design landscape that could lead in the future to a new way to determine good starting points for subsequent local optimization. While in optimization the focus is usually only on local minima, here we show that points selected in the vicinity of other types of critical points (i.e. points where the merit function gradient vanishes) can be very useful starting points. We study here a problem that is simple enough to be analyzed in detail, the design landscape of triplets with variable curvatures. We show here how representatives of all triplet design shapes observed in global optimization runs can be obtained in a simple and systematic way by locally optimizing for each design shape one starting point obtained with the new method. Good approximations of these special starting points are also computed analytically with two theoretical models. We have found a one-to-one correspondence between the possible triplet design shapes and the critical points resulting from a model based on third-order spherical aberration within the framework of thin-lens theory. The same number and properties of critical points are predicted by a second model, which is even simpler and mathematically more general.","saddle point; critical point; global optimization; optical system design","en","conference paper","SPIE","","","","","","","","Applied Sciences","Optics Research Groep","","","",""
"uuid:27451d1b-65e4-440e-a9e0-ffa1fdb489b3","http://resolver.tudelft.nl/uuid:27451d1b-65e4-440e-a9e0-ffa1fdb489b3","Systematics of the design shapes in the optical merit function landscape","Bociort, F.; Van Grol, P.","","2010","In this paper we describe new properties of the design landscape that could lead in the future to a new way to determine good starting points for subsequent local optimization. While in optimization the focus is usually only on local minima, here we show that points selected in the vicinity of other types of critical points (i.e. points where the merit function gradient vanishes) can be very useful starting points. We study here a problem that is simple enough to be analyzed in detail, the design landscape of triplets with variable curvatures. We show here how representatives of all triplet design shapes observed in global optimization runs can be obtained in a simple and systematic way by locally optimizing for each design shape one starting point obtained with the new method. Good approximations of these special starting points are also computed analytically with two theoretical models. We have found a one-to-one correspondence between the possible triplet design shapes and the critical points resulting from a model based on third-order spherical aberration within the framework of thin-lens theory. The same number and properties of critical points are predicted by a second model, which is even simpler and mathematically more general.","saddle point; critical point; global optimization; optical system design","en","conference paper","SPIE","","","","","","","","Applied Sciences","Optics Research Groep","","","",""
"uuid:5aa7303a-d75f-4893-9549-320ddf741662","http://resolver.tudelft.nl/uuid:5aa7303a-d75f-4893-9549-320ddf741662","Finding order in the design landscape of simple optical systems","Van Grol, P.; Bociort, F.; Van Turnhout, M.","","2009","Contrary to the frequent tacit assumption that the local minima of a merit function are points scattered more or less randomly over the design landscape, we have found that, at least for simple imaging systems (doublets with three and triplets with five variables) all design shapes we have observed thus far form a strictly ordered set of points, the “fundamental network”. The design shapes obtained for practical specifications with global optimization algorithms are a subset of the set of local minima in the fundamental network and are organized in a way that can be understood on the basis of the fundamental network","saddle point; global optimization; optical system design","en","conference paper","SPIE","","","","","","","","Applied Sciences","Optics Research Group","","","",""
"uuid:4323c866-c5ca-4956-904c-b0d27dbb70b0","http://resolver.tudelft.nl/uuid:4323c866-c5ca-4956-904c-b0d27dbb70b0","Finding new local minima in lens design landscapes by constructing saddle points","Bociort, F.; Van Turnhout, M.","","2009","","saddle point; global optimization; optical system design","en","journal article","SPIE","","","","","","","","Applied Sciences","Optics Research Group","","","",""
"uuid:6c6197bd-5757-428a-9d3d-e94af148ce90","http://resolver.tudelft.nl/uuid:6c6197bd-5757-428a-9d3d-e94af148ce90","A systematic analysis of the optical merit function landscape: Towards improved optimization methods in optical design","Van Turnhout, M.","Urbach, H.P. (promotor); Bociort, F. (promotor)","2009","A major problem in optical system design is that the optical merit function landscape is usually very complicated, especially for complex design problems where many minima are present. Finding good new local minima is then a difficult task. We show however that a certain degree of order is present in the optical design space, which is best observed when we consider not only local minima, but saddle points as well. With a special method, which we call Saddle-Point Construction (SPC), saddle points can be constructed in a simple way. Via saddle points, new local minima can be obtained very rapidly. When using a local optimization method, the final design after optimization highly depends on the starting configuration. We can group the initial configurations that lead to a given local minimum after local optimization into a graphical region, which shape depends on the optimization method used. However, saddle points are critical points in the merit function landscape that always remain on the boundaries, independent of the used optimization method. When the local optimization process is not chaotic, the geometric decomposition of the space of initial configurations into discrete regions has boundaries given by simple curves. But when the optimization is chaotic, the curves separating the different regions are very complicated objects termed fractals. In such cases, starting configurations, which are very close to each other, lead to different local minima after optimization. A better understanding of these instabilities can be obtained by using low damping values in a damped least-squares method.","optical system design; saddle point; optimization; fractal; chaos","en","doctoral thesis","","","","","","","","","Applied Sciences","","","","",""
"uuid:7cd0b27c-f95b-47c3-969b-36c4b7affa0d","http://resolver.tudelft.nl/uuid:7cd0b27c-f95b-47c3-969b-36c4b7affa0d","Saddle-point construction in the design of lithographic objectives, part 2: Application","Marinescu, O.; Bociort, F.","","2008","","saddle point; lithography; optimization; optical system design; EUV; DUV","en","journal article","SPIE","","","","","","","","Applied Sciences","Optics Research Group","","","",""
"uuid:f16b0c66-bef3-46f9-a84c-174c0e0bc449","http://resolver.tudelft.nl/uuid:f16b0c66-bef3-46f9-a84c-174c0e0bc449","Saddle-point construction in the design of lithographic objectives, part 1: Method","Marinescu, O.; Bociort, F.","","2008","","saddle point; lithography; optimization; optical system design; EUV; DUV","en","journal article","SPIE","","","","","","","","Applied Sciences","Optics Research Group","","","",""
"uuid:28b2169c-2dc0-4258-b572-8c2320cf81d1","http://resolver.tudelft.nl/uuid:28b2169c-2dc0-4258-b572-8c2320cf81d1","Practical guide to saddle-point construction in lens design","Bociort, F.; Van Turnhout, M.; Marinescu, O.","","2007","Saddle-point construction (SPC) is a new method to insert lenses into an existing design. With SPC, by inserting and extracting lenses new system shapes can be obtained very rapidly, and we believe that, if added to the optical designer’s arsenal, this new tool can significantly increase design productivity in certain situations. Despite the fact that the theory behind SPC contains mathematical concepts that are still unfamiliar to many optical designers, the practical implementation of the method is actually very easy and the method can be fully integrated with all other traditional design tools. In this work we will illustrate the use of SPC with examples that are very simple and illustrate the essence of the method. The method can be used essentially in the same way even for very complex systems with a large number of variables, in situations where other methods for obtaining new system shapes do not work so well.","optical system design; optimization; saddle points","en","conference paper","SPIE","","","","","","","","Applied Sciences","Optics Research Group","","","",""
"uuid:c05ad7d6-5504-4fa4-a14f-496e9bb20928","http://resolver.tudelft.nl/uuid:c05ad7d6-5504-4fa4-a14f-496e9bb20928","Predictability and unpredictability in optical system optimization","Van Turnhout, M.; Bociort, F.","","2007","Local optimization algorithms, when they are optimized only for speed, have in certain situations an unpredictable behavior: starting points very close to each other lead after optimization to different minima. In these cases, the sets of points, which, when chosen as starting points for local optimization, lead to the same minimum (the so-called basins of attraction), have a fractal-like shape. Before it finally converges to a local minimum, optimization started in a fractal region first displays chaotic transients. The sensitivity to changes in the initial conditions that leads to fractal basin borders is caused by the discontinuous evolution path (i.e. the jumps) of local optimization algorithms such as the damped-least-squares method with insufficient damping. At the cost of some speed, the fractal character of the regions can be made to vanish, and the downward paths become more predictable. The borders of the basins depend on the implementation details of the local optimization algorithm, but the saddle points in the merit function landscape always remain on these borders.","optimization; optical system design; saddle points; fractals; basins of attraction","en","conference paper","SPIE","","","","","","","","Applied Sciences","Optics Research Group","","","",""
"uuid:ea7af067-bd46-48c8-a147-fe4cddc936ec","http://resolver.tudelft.nl/uuid:ea7af067-bd46-48c8-a147-fe4cddc936ec","Looking for order in the optical design landscape","Bociort, F.; Van Turnhout, M.","","2006","In present-day optical system design, it is tacitly assumed that local minima are points in the merit function landscapewithout relationships between them. We will show however that there is a certain degree of order in the design landscapeand that this order is best observed when we change the dimensionality of the optimization problem and when weconsider not only local minima, but saddle points as well. We have developed earlier a computational method fordetecting saddle points numerically, and a method, then applicable only in a special case, for constructing saddle points by adding lenses to systems that are local minima. The saddle point construction method will be generalized here and wewill show how, by performing a succession of one-dimensional calculations, many local minima of a given global searchcan be systematically obtained from the set of local minima corresponding to systems with fewer lenses. As a simpleexample, the results of the Cooke triplet global search will be analyzed. In this case, the vast majority of the saddlepoints found by our saddle point detection software can in fact be obtained in a much simpler way by saddle point construction, starting from doublet local minima.","saddle point; optimization; optical system design; lithography","en","conference paper","SPIE","","","","","","","","Applied Sciences","Optics Research Groep","","","",""
"uuid:cdd281b2-0bc7-4f57-a9fb-3ddbe49c1082","http://resolver.tudelft.nl/uuid:cdd281b2-0bc7-4f57-a9fb-3ddbe49c1082","Designing lithographic objectives by constructing saddle points","Marinescu, O.; Bociort, F.","","2006","Optical designers often insert or split lenses in existing designs. Here, we present, with examples from Deep and Extreme UV lithography, an alternative method that consists of constructing saddle points and obtaining new local minima from them. The method is remarkable simple and can therefore be easily integrated with the traditional design techniques. It has significantly improved the productivity of the design process in all cases in which it has been applied so far.","saddle point; lithography; optical system design; optimization; DUV; EUV","en","conference paper","SPIE","","","","","","","","Applied Sciences","Optics Research Group","","","",""
"uuid:05dfafdc-cd7c-4b17-a92f-8420e5bb78a0","http://resolver.tudelft.nl/uuid:05dfafdc-cd7c-4b17-a92f-8420e5bb78a0","Generating saddle points in the merit function landscape of optical systems","Bociort, F.; Van Turnhout, M.","","2005","Finding multiple local minima in the merit function landscape of optical system optimization is a difficult task, especially for complex designs that have a large number of variables. We discuss here a method that enables a rapid generation of new local minima for optical systems of arbitrary complexity. We have recently shown that saddle points known in mathematics as Morse index 1 saddle points can be useful for global optical system optimization. In this work we show that by inserting a thin meniscus lens (or two mirror surfaces) into an optical design with N surfaces that is a local minimum, we obtain a system with N+2 surfaces that is a Morse index 1 saddle point. A simple method to compute the required meniscus curvatures will be discussed. Then, letting the optimization roll down on both sides of the saddle leads to two different local minima. Often, one of them has interesting special properties.","saddle point; optimization; optical system design; lithography","en","conference paper","SPIE","","","","","","","","Applied Sciences","Optics Research Groep","","","",""
"uuid:ab738b03-b906-4dc7-9e9c-6ac16446af10","http://resolver.tudelft.nl/uuid:ab738b03-b906-4dc7-9e9c-6ac16446af10","Saddle points in the merit function landscape of lithographic objectives","Marinescu, O.; Bociort, F.","","2005","The multidimensional merit function space of complex optical systems contains a large number of local minima that are connected via links that contain saddle points. In this work, we illustrate a method to construct such saddle points with examples of deep UV objectives and extreme UV mirror systems for lithography. The central idea of our method is that, at certain positions in a system with N surfaces that is a local minimum, a thin meniscus lens or two mirror surfaces can be introduced to construct a system with N+2 surfaces that is a saddle point. When the optimization goes down on the two sides of the saddle point, two minima are obtained. We show that often one of these two minima can be reached from several other saddle points constructed in the same way. The practical advantage of saddle-point construction is that we can produce new designs from the existing ones in a simple, efficient and systematic manner.","saddle point; lithography; optimization; optical system design; EUV","en","conference paper","SPIE","","","","","","","","Applied Sciences","Optics Research Groep","","","",""
"uuid:1e3ce36d-f1f6-4fbd-9349-42ba2352d668","http://resolver.tudelft.nl/uuid:1e3ce36d-f1f6-4fbd-9349-42ba2352d668","The network structure of the merit function space of EUV mirror systems","Marinescu, O.; Bociort, F.","","2005","The merit function space of mirror systems for EUV lithography is studied. Local minima situated in a multidimensional merit function space are connected via links that contain saddle points and form a network. In this work we present the first networks for EUV lithographic objectives and discuss how these networks change when control parameters, such as aperture and field are varied and constraints are used to limit the variation domain of the variables. A good solution in a network obtained with a limited number of variables has been locally optimized with all variables to meet practical requirements.","network; saddle point; optical system design; EUV lithography; optimization","en","conference paper","SPIE","","","","","","","","Applied Sciences","Optics Research Groep","","","",""
"uuid:3c613301-54f1-4fe0-bfa4-9793fa751d5f","http://resolver.tudelft.nl/uuid:3c613301-54f1-4fe0-bfa4-9793fa751d5f","Correction of the phase retardation caused by intrinsic birefringence in deep UV lithography","Serebriakov, A.; Bociort, F.; Braat, J.","","2005","In the year 2001 it was reported that the birefringence induced by spatial dispersion (BISD), sometimes also called intrinsic birefringence, had been measured and calculated for fluorides CaF2 and BaF2 in the deep UV range. It was also shown that the magnitude of the BISD in these cubic crystals is sufficiently large to cause serious problems when using CaF2 for lithographic objectives at 157 nm and possibly also in the case of high numerical aperture immersion objectives at 193 nm. Nevertheless the single-crystal fluorides such as CaF2 are the only materials found with sufficient transmissivity at 157 nm and they are widely used at 193 nm for chromatic correction. The BISD-caused effects lead to the loss of the image contrast. In this work we discuss issues related to the design of optical systems considering the BISD effect. We focus on several approaches to the compensation of the BISD-related phase retardation and give examples of lithographic objectives with the compensated phase retardation","lithography; birefringence; spatial dispersion; phase retardation; optical system design","en","conference paper","SPIE","","","","","","","","Applied Sciences","Optics Research Groep","","","",""
"uuid:c32dbcf1-d0d8-491e-81ae-d959d3ffd228","http://resolver.tudelft.nl/uuid:c32dbcf1-d0d8-491e-81ae-d959d3ffd228","Saddle points in the merit function landscape of systems of thin lenses in contact","Bociort, F.; Serebriakov, A.; Van Turnhout, M.","","2004","The merit function landscape of systems of thin lenses in contact, which are perhaps the simplest possible types of optical systems, shows remarkable regularities. It is easier to understand how the optimization parameter space of these simple systems is divided into basins of attraction for the various local minima if one focuses on the (Morse index 1) saddle points in the landscape rather than on the local minima themselves. The existence and the basic properties of these saddle points can be predicted by thin-lens theory, which is applied on a simplified model of the merit function containing only third-order spherical aberration. The predictions of this simplified model are confirmed by numerical results obtained with a typical merit function based on ray tracing.","global optimzation; saddle points; thin lens theory; spherical aberration; optical system design","en","conference paper","SPIE","","","","","","","","Applied Sciences","Optics Research Groep","","","",""
"uuid:adfd90ba-e76a-498c-8cc4-43ef7289c135","http://resolver.tudelft.nl/uuid:adfd90ba-e76a-498c-8cc4-43ef7289c135","The effect of intrinsic birefringence in deep UV-lithography","Serebriakov, A.; Maksimov, E.; Bociort, F.; Braat, J.","","2004","The subject of birefringence induced by spatial dispersion (BISD), also called intrinsic birefringence, recently became an important issue for 157-nm lithography. For the deep UV range, because of intrinsic absorption, only crystalline materials can be used as optical materials for lens manufacturing. The physical properties of crystals are basically affected by spatial dispersion, especially at very short wavelengths. The resulting BISD leads to a serious deterioration of optical image quality. Recently the mathematical formalism for analyzing those aspects of the BISD effect that are relevant for optical design has been published. In this work we give an equivalent but simplified derivation of these results. This mathematical formalism is then applied to optical system design and the correction methodology is discussed. An example of optical system is given that has been corrected for the BISD effect.","lithography; briefringence; crystal; optical system design","en","conference paper","SPIE","","","","","","","","Applied Sciences","Optics Research Groep","","","",""
"uuid:440be13a-ffb8-4e24-aa39-1d52ad2a0d4b","http://resolver.tudelft.nl/uuid:440be13a-ffb8-4e24-aa39-1d52ad2a0d4b","Topography of the merit function landscape in optical system design","van Driel, E.; Bociort, F.; Serebriakov, A.","","2004","We have shown recently that, when certain quite general conditions are satisfied, the set of local minima in the optical merit function space forms a network where they are all connected through optimization paths generated from saddle points having a Morse index of 1. A new global optimization method, that makes use of this linking network to systematically detect all minima, is presented. The central component of this new method, the algorithm for saddle point detection, is described in detail and we show that the initialization of this algorithm has a significant impact on the performance. For a simple global optimization search (Cooke triplet) several representation forms of the network of the corresponding set of local minima are presented. These representations, which can be visualized in two dimensions, are independent of the dimensionality of the design space so that they can provide insight into the topography of merit function landscapes of arbitrary dimensionality.","global optimization; saddle point; Morse index; network; optical system design","en","conference paper","SPIE","","","","","","","","Applied Sciences","Optics Research Groep","","","",""